Efficient use of the radio spectrum is crucial for the successful operation of integrated terrestrial networks (TNs) and non-terrestrial networks (NTNs). The dynamic and heterogeneous nature of these integrated TN-NTN networks presents significant challenges to spectrum efficiency, primarily due to non-stationary interference patterns and the coexistence of diverse network types. Dynamic spectrum management (DSM) emerges as a viable approach to address these challenges, and within this context, artificial intelligence (AI) offers a powerful way of enabling optimal spectrum sharing. This chapter explores how machine learning algorithms—specifically deep learning, reinforcement learning, and large language models—can predict spectrum occupancy and adaptively allocate spectrum resources. It incorporates careful consideration of the diverse characteristics of TN and NTN signals, particularly the Doppler shifts and latency issues associated with high altitude platforms (HAPs) and satellite links. We examine how AI can mitigate interference between TNs and NTNs while exploring methods to improve overall network spectral efficiency. Finally, we identify the algorithmic and practical challenges of designing intelligent agents capable of collaboratively negotiating spectrum access and sharing among various network operators and devices, and suggest potential future research directions.